After reading the question why do I only breathe out of one nostril I realized that breathing out of both isn't common. I have always breathed out of both, and when I get a stuffy nose, or a runny nose, it's on both sides. If only one side is stuffed, I'll just lay on my side a bit to even it out until I can breathe out of both again. I've always though that was totally normal! What does it mean that my autonomous nervous system is not alternating my breathing?
The odds are that you're noticing the equality of patent nostrils in the middle of a changeover, when both are equally patent. Also, the shape of your nose may be permitting the congested side to still be fairly patent. Your nose is doing what it's supposed to be doing (and everybody suffers bilateral congestion during colds, allergies, etc.) If it were not, you would be plagued by dry, painful and bleeding nares (um... are you?)